{
  "id": "1203.3905",
  "version": "v1",
  "published": "2012-03-17T23:23:58.000Z",
  "updated": "2012-03-17T23:23:58.000Z",
  "title": "Driven Brownian coagulation of polymers",
  "authors": [
    "P. L. Krapivsky",
    "Colm Connaughton"
  ],
  "comment": "14 pages and 12 figures",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We present an analysis of the mean-field kinetics of Brownian coagulation of droplets and polymers driven by input of monomers which aims to characterize the long time behavior of the cluster size distribution as a function of the inverse fractal dimension, $a$, of the aggregates. We find that two types of long time behavior are possible. For $0\\leq a < 1/2$ the size distribution reaches a stationary state with a power law distribution of cluster sizes having exponent 3/2. The amplitude of this stationary state is determined exactly as a function of $a$. For $1/2 < a \\leq 1$, the cluster size distribution never reaches a stationary state. Instead a bimodal distribution is formed in which a narrow population of small clusters near the monomer scale is separated by a gap (where the cluster size distribution is effectively zero) from a population of large clusters which continue to grow for all time by absorbing small clusters. The marginal case, $a=1/2$, is difficult to analyze definitively, but we argue that the cluster size distribution becomes stationary and there is a logarithmic correction to the algebraic tail.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-03-17T23:23:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "36.40.Mr",
      "36.20.Hb",
      "36.20.Ey",
      "31.15.X-"
    ],
    "keywords": [
      "driven brownian coagulation",
      "cluster size distribution",
      "stationary state",
      "long time behavior",
      "small clusters"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1063/1.4718833",
      "journal": "Journal of Chemical Physics",
      "year": 2012,
      "month": "May",
      "volume": 136,
      "number": 20,
      "pages": 4901
    },
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012JChPh.136t4901K"
    }
  }
}